Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9540

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9540 – $5300 = $4240

Thus, Simple Interest = $4240

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4240}/_{5300 × 10}

= ⁴²⁴⁰⁰⁰/₅₃₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5300

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4240 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 10% of Principal

= 10% of $5300

= ¹⁰/₁₀₀ × 5300

= ^{10 × 5300}/₁₀₀

= ⁵³⁰⁰⁰/₁₀₀ = 530

Thus, simple Interest for 1 year = $530

Now,

∵ If the simple Interest is $530, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₀ years

∴ If the simple Interest is $4240, then the time = ¹/₅₃₀ × 4240 years

= ^{1 × 4240}/₅₃₀ years

= ⁴²⁴⁰/₅₃₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(2) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.

(4) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3000 will amount to $3300 at a simple interest of 5% per annum?

(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

(7) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(10) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.